Stability
My Definition: An LTI system is stable if it does not get extremely large as time goes to infinity.
Example Unstable: $ y(t) = e^{-6t}*u(3-t) $
$ \int_{-\infty}^\infty |y(t)| dt $ $ \int_{-\infty}^3 e^{-6t} dt = \infty $ $ \Rightarrow y(t)\rightarrow \infty $
Therefore, the system is unstable because it gets extremely large as time goes to infinity.
Example Stable: $ y(t) = e^{-2t}*u(t+50) $
$ \int_{-\infty}^\infty |y(t)| dt $ $ \int_{-50}^\infty e^{-2t} dt $ $ = -\dfrac{1}{2}e^{-2t}|_{-50}^\infty $ $ = \dfrac{e^{100}}{2} < \infty $
Therefore, the system is stable because it goes to a finite number as time goes to infinity.
